Inverse Trigonometric Functions Practice Test

In a right triangle, $\cos(\theta)=\frac{5}{13}$ with $0^\circ<\theta<90^\circ$. Use an inverse trigonometric function to find $\theta$ in degrees to the nearest tenth.

A ship travels 7 km east, then 9 km north, forming a right triangle with legs 7 and 9. The angle $\theta$ between the ship’s final displacement and the east direction satisfies $\tan(\theta)=\frac{9}{7}$. Find $\theta$ in degrees (nearest tenth).